This is exactly what happened to me during my last pregnancy. Try not to worry too much, it doesn't normally affect the baby unless it goes unmonitored, which is why they do the routine bloodwork in the first trimester. They may or may not treat it with PTU and it may normalize itself during the 2nd trimester.
Here is my thyroid journey so you're aware of what to watch out for and can speak up if need be:
I was told I had a low TSH and was diagnosed with hyperthyroidism late in the first trimester of my last (3rd) pregnancy. I've never had thyroid problems before that. I had a couple episodes where my heart was racing, I got extremely hot and felt like I was going to vomit, followed by cold sweats and no energy to even pick myself up off the floor. I went to an endocrinologist who wanted to monitor it but not treat it with meds, but my OB wanted it treated since I had a couple scary episodes, so I got a 2nd opinion which was the same as the first - monitor but not treat. The first endo treated with a low dose of PTU after my OB insisted. I felt better after it kicked in a couple weeks later. But, that was short-lived. A couple weeks after that, I had very little energy, even after getting a good night's sleep I'd wake up unrefreshed and worn out. I got to the point where it was so bad, I could barely take care of myself, let alone my 2-year-old and I barely escaped bedrest. Taking a microwave dinner out of the freezer, putting it in the microwave and getting up to get it out when it was done cooking was too much energy expended for the day, and of course, that's not all I had to do every day. And, if I used too much energy one day, it would get compounded and carry into the next day, so I'd be at a deficit and was on a downward spiral that I just couldn't catch up no matter what I did or didn't do. I also couldn't stand for more than 2 minutes without getting dizzy and feeling like I was going to pass out - every time. So, I couldn't run errands, go grocery shopping, stand in line, stand to prepare or cook dinner, or even stand long enough to peel an orange over the garbage can. It wasn't so much that I was tired and needed to get more sleep, which no one seemed to understand, it was just a feeling of being completely worn out, which is different. It was more like I was doing too much manual labor and my body needed to take a break, except that it was all day every day, and sleep never replenished my energy level like it does when I'm "normal." It was horrible and I almost ended up on bedrest for the last 3 months of my pregnancy after putting myself on a modified bedrest for a couple months before that in an effort to avoid hospitalized bedrest. My OB said none of that was normal pregnancy stuff, and it was definitely unlike anything I'd experienced during my previous 2 pregnancies, so she sent me to an Internist. Everyone but my OB kept trying to tell me it was just pregnancy-related, but I don't know anyone else who was that close to their deathbed just from being pregnant; my OB was the one who kept me sane and agreed with me that something else was wrong. I was tested for everything under the sun - Cardiomyopathy, Addison's disease, adrenal problems, heart problems, lung problems, infection, lupus, and a bazillion other things, and sent to a cardiologist, pulmonologist, another endocrinologist and was going to be referred to a neurologist next to test for multiple sclerosis. It was a nightmare! I'm not a violent person, but after about the 3rd time that the Internist tried to convince me "maybe it's a boy this time" and imply that it's just normal pregnancy stuff that I didn't experience with my girls, I had to refrain from punching him, but I didn't have the energy anyway.
All the while, everyone, including the endocrinologists, refused to believe it had anything to do with my thyroid since I was being treated for my hyperthyroidism and my symptoms were not classic to thyroid problems. I lost 4 months of my life to extreme health challenges and I am normally the person who manages to stay healthy and avoid getting colds, the flu, etc. that goes around, even when members of my family are sick, or I don't get it as bad as everyone else. I'm NEVER sick!
It turned out to be hypothyroidism that was complicated by the PTU (hyperthyroid meds for the opposite problem). What had happened was I started out hyperthyroid in the first trimester, then during the 2nd trimester my thyroid normalized itself, and then my thyroid went hypothyroid - all while I was still on the hyperthyroid meds. I only realized what was going on after the fact when I raised the question with my Internist that it has to be something obvious that is being overlooked, and he sent me to another endocrinologist. Even she said it wasn't my thyroid nor the hyper meds that were causing my health issues, but she agreed to let me stop them since they were suppressing my thyroid and I was having extreme energy issues, and frankly, I told her I refused to take them anymore because I couldn't bare the thought of supressing my energy level anymore when I was already at a deficit. Within 2 1/2 weeks of stopping the PTU (the time it took for the meds to initially take effect), all of my debilitating symptoms disappeared and I finally felt normal-pregnant into the last trimester with no relapse of debilitating symptoms. Ironically, after being off the meds for a while, I was diagnosed with hypothyroidism and the endocrinologist wanted to put me on hypo meds at 36 weeks pregnant. She STILL refuses to believe that my health problems were caused by the hyper meds, so she can't seem to understand my concern about the possibility of going hyperthyroid again post-pardum, since I have run the spectrum between hyper and hypothyroidism and have no previous thyroid conditions to point to to even take a guess as to where it's going to end up post-pardum. I refused the meds, had the baby at 37 weeks (due to low amniotic fluid, not related to my thyroid problems), and agreed to get my thyroid rechecked at one month post-pardum and decide then what to do if my thyroid was still a problem. I'm 8 weeks post-pardum now and am still hypothyroid as of my one-month post-pardum labs, and am dealing with the classic symptoms of hypothyroidism, which is tiring but nowhere near as debilitating as my previous symptoms. My endo is only in on Wednesdays, so I'm expecting a call tomorrow to determine whether or not she wants to put me on meds for it. I'm still undecided if I will take them or not at this point or wait it out longer.
I tell you this not to scare you by any means, but so that you're aware that first of all, they may or may not put you on meds right away, but as long as they monitor your thyroid so it doesn't go too far one way or the other, you and the baby will be fine, so try not to worry. Secondly, if they do put you on meds, just be aware that your thyroid may normalize itself during the 2nd trimester or it may go hypothyroid with or without the hyper meds. If they do put you on meds and you start to have any symptoms that are causing you issues (even months later), insist on stopping the meds for a few weeks to see if it helps any (they don't kick in or go away immediately, it takes a couple weeks), even if they insist it's not your thyroid or the meds that are causing your symptoms. (My labs were within the normal ranges on the PTU when I was having all of my health issues and only slightly hypothyroid at the end of it. I'm not sure how that happened since my symptoms were so extreme, but somehow I think the meds masked the labs so I didn't get true results.)
BTW, I had a healthy baby boy (1st boy for me after 2 girls) who has no issues whatsoever from my thyroid problems during my pregnancy. As part of the normal newborn screening in the hospital, they always check their thyroid levels, so there isn't anything extra that they need to do once your baby is born. They will, however, monitor your pregnancy more closely and you will probably have one or 2 more ultrasounds after your normal 18-20 weeks ultrasound as a precaution. Not a bad thing since you get to see your baby more.